Cześć! I am a third year PhD Student at University of California Los Angeles (UCLA). I'm a part of the probability research group working with professors Georg Menz and Marek Biskup. I am also the lead developer of Agrade, a system for grading automation being tested at UCLA math department. But my main love are various particle systems. See below what fun they are!

Model

Research

Probability theory: interacting particle systems, stochastic dynamics and statistical mechanics, and, more recently, AI-assisted verification and assessment of mathematical work.

Interacting particle systems

Ergodicity and decay of correlations for one-dimensional interacting particle systems: a time-scaling argument extending classical ergodicity criteria, a recursive criterion for covariance decay, and an ergodicity criterion for one-sided systems with a long-lived state. Motivated by the positive rates conjecture; models of interest include the East model with noise and multi-stage contact processes. Joint with Georg Menz.

Disordered Ising models

Random-current and transfer-matrix methods for the one-dimensional heterogeneous Ising model with signed (ferro- and antiferromagnetic) interactions, giving correlation bounds for disordered systems. Joint with Edward Athaide, Jonas Köppl and Georg Menz.

Branching Brownian particles with resource recycling

Current project: a spatial population of Brownian particles that reproduce at a rate set by an immobile resource which they consume, with each death returning resource at the death location. The recycling balance \(\theta=\beta m/c\) decides survival from finite states and growth or decay of the large-population limit. Advised by Georg Menz in collaboration with Marek Biskup.

Interacting AI agents for mathematical reliability

AGrade: an agentic, multi-agent AI grading system I develop with Georg Menz, in production in the UCLA Mathematics Department (Summer 2026 GSR appointment funded through IPAM). Building on it, Proof Crystallization (with Georg Menz and Guido Montúfar): an agentic preprocessing layer between informal LLM-generated mathematics and formal verification in Lean, organizing agents into construction, verification, adversarial critique, repair and judgment roles.

Publications

Preprints

A Sharp Survival Threshold for Branching Brownian Motion in a Self-Generated Resource Environment

M. Głuchowski, G. Menz

arXiv preprint2026 Branching Brownian motionResource environmentSurvival thresholdBranching processes

arXiv PDF

Published

Ergodicity Criterion for One-Sided, One-Dimensional IPS with a Long-Lived State

M. Głuchowski, G. Menz

Electronic Communications in Probability2026 Interacting Particle SystemsErgodicityPositive rates conjecture

ECP arXiv PDF

A Correlation Bound for the One-Dimensional Heterogeneous Ising Model

E. Athaide, M. Głuchowski, J. Köppl, G. Menz

Electronic Communications in Probability2026 Random Ising modelAntiferromagneticDisordered systemsDecay of correlationsRandom currentsTransfer matrix

ECP arXiv PDF

Time-Scaling, Ergodicity, and Covariance Decay of Interacting Particle Systems

M. Głuchowski, G. Menz

Journal of Statistical Physics2025 Interacting Particle SystemsErgodicityInvariant measureDecay of correlationsPositive rates conjectureTwo-stage contact process

JSP arXiv PDF

Talks

Upcoming

Title TBA - AMS Fall Western Sectional Meeting, Special Session on Lattice Models of Statistical Mechanics (associated with the Invited Address by Thomas Hutchcroft), Arizona State University, Tempe, AZ, November 7-8, 2026

Past

"Vibe code your agent" - UCLA Thursday Colloquium and AI in Research and Education Seminar, June 2026
"Ergodicity of the East model with noise" - UCLA Probability Seminar, 2025
"Progress on the positive rates conjecture" - UCLA informal seminar, 2023
"Ergodicity of interacting particle systems" - Analysis in the Tatras 2023, Małe Ciche (University of Warsaw)
"Introduction to the positive rates conjecture" - Beyond the Horizon 2022, Będlewo (IMPAN)
"Collective memory" - Beyond the Horizon 2021, Będlewo (IMPAN)